Another approach to derive predefined-time consensus algorithms has been addressed via a linear function of the sum of the errors between neighboring nodes together with a time-varying gain, for instance, using time base generators [1]}, see e.g., [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}. However, these methods require that all nodes have a common time-reference because the same value of the time-varying gain should be applied to all nodes. Thus, this approach is not suitable in GPS-denied environments or in scenarios where having a common time reference is a strong assumption. Moreover, such time-varying gain becomes singular at the pre-set time, either because the gain goes to infinite as the time tends to the pre-set time [2]}, [7]} or because it produces Zeno behavior (infinite number of switching in a finite-time interval) as the time tends to the pre-set time [3]}.
